Mercerian theorems via spectral theory

On Some Mercerian Theorems in Summability

Security Theorems via Model Theory

A model-theoretic approach can establish security theorems, which are formulas expressing authentication and non-disclosure properties of protocols. Security theorems have a special form, namely quantified implications ∀~x .(φ ⊃ ∃~y .ψ). Models (interpretations) for these formulas are skeletons, partially ordered structures consisting of a number of local protocol behaviors. Realized skeletons ...

Tauberian and Mercerian Theorems for Systems of Kernels

In [BI3], we introduced the notion of ratio Mercerian theorem, to improve the Mercerian theorem for Fourier and Hankel transforms first proved in [BI1]. In the first half of this paper, we extend (and correct) the ratio Mercerian theorem, and apply it to the proofs of Tauberian theorems for kernels of Korenblum type. The latter can be applied to analytic number theory; this was in fact the moti...

Weyl ’ S Theorems and Local Spectral Theory 3

We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl’s theorem and a-Weyl’s theorem. We show that if T or T ∗ has SVEP and T is transaloid, then Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )). When T ∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T ...

Spectral Theory and Limit Theorems for Geometrically Ergodic Markov Processes

Consider the partial sums {St} of a real-valued functional F (Φ(t)) of a Markov chain {Φ(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the following conclusions are obtained: Spectral theory: Well-behaved solutions f̌ can be constructed for the “multiplicative Poisson equation” (eP )f̌ = λf̌ , where P is...